Question

which diagram shows lines that must be parallel lines cut by a transversal? 89° 89° 91° 91°

Explanation:

Step1: Recall the converse of the corresponding angles postulate

If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.

Step2: Analyze the first diagram

In the first diagram, we have two angles of \(89^{\circ}\). These angles are corresponding angles. Since they are congruent (\(89^{\circ}=89^{\circ}\)), by the converse of the corresponding angles postulate, the lines \(m\) and \(r\) (or \(m\) and \(s\)) are parallel.

Step3: Analyze the second diagram

In the second diagram, we have two angles of \(91^{\circ}\). But these angles are not in a position of corresponding angles (they are not in the same relative position with respect to the transversal and the two lines). So we cannot use the converse of the corresponding - angles postulate to conclude that the lines are parallel.

Answer:

The first diagram.